# Mechanical Behaviors of a Symmetrical Bolt Fasten Wedge Active Joint for Braced Excavations

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of the BFW Active Joint

#### 2.1. Basic Function of Active Joints

_{SI}should be smaller than the excavation length l

_{EI}such that the steel tubes can be put into the pit. In other words, there is a gap between the steel tube and the retaining structure. Simultaneously, an extra length is needed to fill this gap. An active joint is designed to play the role of this part. This active joint should have a large extension length with the help of a hydraulic jack, which can bring the steel bracing close to the side wall of the foundation pit, and the pre-axial force can be achieved. The steel bracing with the active joint should be able to be stressed separately after the jack as a tool is removed. In addition, the designed active joint should be self-locking without any other spare parts. Furthermore, in the demolition process, the active joint should be able to be shorten in length to eliminate the internal force of the steel bracings and facilitate the demolition of the steel bracings.

- Before deformation (installation): l
_{EI}—excavation width, l_{SI}—total length of the steel tube, l_{AI}—length of the active joint, and l_{GI}—length of the reserved gap. - In deformation (working): l
_{EW}—excavation width, l_{SW}—total length of the steel tube, and l_{AW}—length of the active joint. - After deformation (demolition): l
_{ED}—excavation width, l_{SD}—total length of the steel tube, l_{AD}—length of the active joint, and l_{GD}—length of the demolition required gap.

#### 2.2. Components and Composition

_{0}) state before it is installed in site, and it will be in an arbitrary extension (l

_{arb}) state when it is applying the intended pre-axial force. However, the maximum extension will be limited to the maximum extension (l

_{max}) state, which may usually meet the requirements of exerting the pre-axial force on the basis of the construction practice of braced excavations.

#### 2.3. Working Mechanism

- F/2: the axial force transferred by the steel tube to each side.
- T: the tension provided by a high-strength bolt, where n is the number of the bolts on one side, and a BFW active joint contains 2n bolts.
- R: the resistance between the splints and the wedge seat.
- V: the supporting force between the splints and the base.
- f: the friction between the bottom of the splints and the base.
- δ: the steel friction angle, where μ is the steel static friction coefficient, and tan δ = μ.
- θ: the angle between the direction of the axial force F/2 and the direction of the contact surface, where the contact surface is between the wedge seat and the splints.

_{d}is calculated under the most unfavorable condition. This condition is defined as when the extension length is the maximum extension l

_{max.}According to the code for the design of steel structures [22], the design tensile bearing capacity of bolts N

_{bt}can be calculated as follows [23]:

_{tube}is the cross-sectional area of the steel tube and A

_{min}is the area of the minimum section of the BFW active joint when under the most unfavorable conditions.

- V
_{i}—the volume of a component of the BFW active joint. - A
_{d}—the cross-sectional area of the column. - h—the length of the BFW active joint.
- m—the number of the components of the BFW active joint.
- i—the component number.

_{d}can be calculated according to Hooke’s law:

## 3. Field Operation Tests

#### 3.1. Design of Specimens

_{max}was 150 mm; P was 570.4 kN; and the other size parameters are shown in Figure 5. Therefore, substituting the parameters into Equations (1)–(7) and Equations (9) and (10), this gives: N

_{bt}was 456.3 kN, the design bearing capacity N of a BFW active joint was 2551 kN, and the design stiffness K

_{d}was 297 kN/mm.

_{max}was 150 mm and A

_{min}was calculated to be 46,219.44 mm

^{2}. The A

_{tube}of the Φ609 mm × 14 mm steel tube was 26,169.47 mm

^{2}and A

_{tube}of the Φ800 mm × 16 mm steel tube was 39,108.14 mm

^{2}. They were both smaller than the A

_{min}, therefore Equation (8) was satisfied. Therefore, the design results satisfied the strength-checking calculation.

#### 3.2. Test Site and Preparation

#### 3.3. Operation Process

- (1)
- The gap was filled with fillers like steel wedges or cement, as shown in Figure 8a. It should be noted that the end plate near the splints must be kept parallel to the vertical plate of the buried tray. If there exists an angle between the two plates, it is necessary to fill the gap with fillers like steel wedges or cement.
- (2)
- The bolts were tightened step-by-step in the process of the jack force application, as shown in Figure 8b. The jack force application consists of three loading stages using a jack pressure gauge, i.e., 5 MPa, 12 MPa, and 25 MPa. Six bolts were fastened one-by-one on each stage. The jack force application was stopped when the loading using the jack pressure gauge reached 25 MPa which met the intended pre-axial force. All the bolts should be fastened at the same level, and the fastened torque should be 4111 Nm. No space should be left between the wedge seat and the splints.
- (3)
- The jack was unloaded and moved away, as shown in Figure 8c, and the BFW active joint started working. The earth pressure transmitted by the lateral walls of the foundation pit were borne by the steel tube bracings with the BFW active joints. The BFW active joints were connected with steel tubes in a series connection and they bore the same axial force as the steel tubes.
- (4)
- The steel tube bracing with the BFW active joint was demolished. The bolts were loosened after the axial force was applied by the jack, as shown in Figure 8d. Then, the BFW active joints were shortened and they were moved out of the pit with the steel tube bracings.

#### 3.4. Analysis of the Field Operation Results

- (a)
- It is important to weld the BFW active joint concentrically with the short steel tube in the pre-processing at the test site.
- (b)
- The total length of the BFW active joint and steel tube is a little smaller than the excavated width of the foundation pit, so a gap of 30–130 mm will be formed. At this time, since the BFW active joint is in the zero-extension state, it can be extended to eliminate the gap during jack force application.
- (c)
- It is necessary to keep the contact surface of the purlin or the diaphragm retaining walls flat and vertical.
- (d)
- It is important to ensure that the loading process is uniform and slow, and that the bolts are tightened to the same tightening torque (4111 Nm for the M39 type). Both the whole loading process and tightening process should be divided into three steps, step-by-step, which can provide a good loading effect. The bolts need to finally be fastened to a tightening torque of 4111 Nm.
- (e)
- The jack is used to supplement the axial force and then the bolts will be tightened according to the above steps once the axial force loss occurs with the variation of soil excavation and earth pressure change.

## 4. Laboratory Axial Compression Experiments

#### 4.1. Measurement Scheme of Displacements and Strains

_{N}and the other side was named D

_{S}, as shown in Figure 9a. Some strain gauges were installed in certain key positions to measure strain changes, shown as S

_{NB1}–S

_{NB3}, S

_{SB1}–S

_{SB3}, S

_{N1}–S

_{N10}, and S

_{S1}–S

_{S10}. Taking one specimen as an example, six strain gauges (S

_{NB1}–S

_{NB3}, S

_{SB1}–S

_{SB3}) were installed on the high-strength bolts in the direction of the bolt axis, and each bolt got one, as shown in Figure 9b; 20 strain gauges (S

_{N1}–S

_{N10}, S

_{S1}–S

_{S10}) were installed on the outer surface of two sides, and each side got 10, as shown in Figure 9c,d. Before sticking the strain gauge on, the surface of the bolts were properly polished.

#### 4.2. Loading Schemes

- (a)
- The specimens were loaded from 0 kN to 500 kN and unloaded back to 0 kN, where the loading rate was 30 kN/min. Gaps in the specimens could be closed in this stage of preloading.
- (b)
- Formal loading and data collection were applied under force control, where the loading rate was 50 kN/min. The loading started from 0 kN. When the bearing capacity of the specimens could no longer rise or had a large deformation or failure, loading was stopped. Then, unloading was slowed down and the test ended.

#### 4.3. Experimental Phenomena and Failure Modes

#### 4.4. Bearing Capacities and Stiffness

#### 4.5. Strain Distributions

_{N1}–S

_{N10}and S

_{S1}–S

_{S10}indicated that the specimens gradually entered the inelastic deformation stage from the elastic deformation stage, then they underwent plastic deformation until their compression and bending failure occurred. The deformation of the main body of the specimens was smaller than that of the bolts, and the stiffness of the main body of the specimens was larger than that of the bolts. However, the degree of deformation of different parts on the main body was not the same, i.e., the positions of S

_{N1}–S

_{N2}, S

_{N7}–S

_{N10}, S

_{S1}–S

_{S2}, and S

_{S7}–S

_{S10}had a greater deformation than the positions of S

_{N3}–S

_{N6}and S

_{S3}–S

_{S6}. Therefore, within the structure, the effect of the axial force was greater than that of the bending moment, and the deformation results provided guidance for optimizing the design scheme. Furthermore, from Figure 13a–c, it was found that the strain of some curves appeared in the opposite direction of the whole trend at a certain stage, then moved back to the whole trend, and even appeared to be almost symmetrical curves in Figure 13c. This phenomenon also proved that the loading device had an eccentric compression; the compression of the two sides was not consistent; and in the direction of the bolts’ axis, there was also a small eccentric compression. As the pressure increased, the eccentric compression of some positions recovered. The eccentric compression in some positions continued to develop due to the structural characteristics, but the overall deformation was in the normal range. Therefore, the load–strain curves at the key positions also proved that the BFW active joint showed a good compression performance and eccentricity resistance.

## 5. Numerical Simulation and Validation

#### 5.1. Numerical Model

^{8}N/mm

^{2}. Because the BFW active joint was assembled using multiple components, there were multiple contact surfaces among the different components. The setup of the contact pairs in the numerical model are listed in Table 3. Most of contact pairs were simulated using a surface-to-surface contact method called a axisymmetric general contact. In this condition, the two objects in the space can be in contact with each other but not through each other, and the two contact surfaces can be separated and contacted. A stiffness coefficient of 1 represents hard contact. The tangent friction force was applied through a penalty method, and according to the handbook of mechanical design [25], the friction coefficient was 0.15. The boundary condition was set up to consolidate the bottom surface of the lower end plate. The loading form was simulated by the loading plate, just like the loading of the laboratory press. A vertical loading was loaded on the surface center of the loading plate, and the automatic-loading-step number was selected in the software to improve the calculation efficiency. Finally, the ultimate loading of the experiment, i.e., 4195 kN, was uniformly loaded in seven steps.

#### 5.2. Comparisons of Numerical and Experimental Results

#### 5.2.1. Failure Modes

#### 5.2.2. Load–Displacement Curves

_{S}curve were 16.70%, 3.74%, and 10.22%, respectively. The deformation of the numerical model was smaller than that of the BFW-AJ2 D

_{S}. In the second half of the plastic section, there was still a certain deviation, but the deviation was not large. The numerical result curve was more similar to the BFW-AJ2 D

_{N}curve. From 2500 kN to 4000 kN, the maximum deviation, minimum deviation, and average deviation between the numerical result curve and the BFW-AJ2 D

_{N}curve were 30.01%, 7.08%, and 18.54%, respectively. The deformation of the numerical model gradually became larger than that of the BFW-AJ2 D

_{N}. The numerical curve was generally among the four test curves. Therefore, more material nonlinearity factors should be considered in further simulations.

#### 5.2.3. Load–Strain Curves

_{B1}and the test curve BFW AJ1 S

_{SB1}were 27.20%, 16.10%, and 21.65%, respectively; the three deviations between the numerical result curve FEM S

_{B2}and the test curve BFW AJ2 S

_{SB2}were 25.21%, 7.12%, and 16.16%, respectively; and the three deviations between the numerical result curve FEM S

_{B3}and the test curve BFW AJ2 S

_{SB3}were 17.54%, 13.46%, and 15.50%, respectively.

_{B1}and the test curve BFW AJ1 S

_{SB1}were 23.23%, 14.00%, and 18.62%, respectively; the three deviations between the numerical result curve FEM S

_{B2}and the test curve BFW AJ1 S

_{NB2}were 25.47%, 8.11%, and 16.79%, respectively; and the three deviations between the numerical result curve FEM S

_{B3}and the test curve BFW AJ2 S

_{SB3}were 14.59%, 2.60%, and 8.60%, respectively. The deviation values showed that the curves simulated using the numerical model were in good agreement with the experimental results, whether using bolt 1, bolt 2, or bolt 3. The numerical simulation results basically accorded with the changing trend of the bolt strain. Therefore, in the subsequent optimization design, the numerical model can be used for fine adjustment and improvement in order to predict the results accurately and save the cost of experimentation.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Tan, Y.; Li, M. Measured performance of a 26 m deep top-down excavation in downtown Shanghai. Can. Geotech. J.
**2011**, 48, 704–719. [Google Scholar] [CrossRef] - Zhang, M.; Yang, M.; Li, P.; Lu, D. An innovative bolt fastener for steel tube bracing in deep excavations. In Proceedings of the China-Europe Conference on Geotechnical Engineering, Vienna, Austria, 13–16 August 2018. [Google Scholar]
- El-Sawy, K.M. Inelastic stability of liners of cylindrical conduits with local imperfection under external pressure. Tunn. Undergr. Space Technol.
**2013**, 33, 98–110. [Google Scholar] [CrossRef] - Feng, R.; Lin, J.; Mou, X. Experiments on hybrid tubular K-joints with circular braces and square chord in stainless steel. Eng. Struct.
**2019**, 190, 52–65. [Google Scholar] [CrossRef] - Lam, E.S.S.; Li, B.; Xue, Z.H.; Leung, K.T.; Lam, J.Y.K. Experimental studies on reinforced concrete interior beam-column joints strengthened by unsymmetrical chamfers. Eng. Struct.
**2019**, 191, 575–582. [Google Scholar] [CrossRef] - Puzrin, A.M.; Alonso, E.E.; Pinyol, N.M. Braced excavation collapse: Nicoll Highway, Singapore. In Geomechanics of Failures; Springer: Dordrecht, The Netherlands, 2010; pp. 151–181. [Google Scholar]
- Endicott, J. Lessons learned from the collapse of the Nicoll Highway in Singapore April 2004; IABSE Symposium Report; International Association for Bridge and Structural Engineering: Zurich, Switzerland, 2013; Volume 101, pp. 1–6. [Google Scholar]
- Li, H.; Wang, G. Causes and suggestion on deep foundation excavation accident in some. Constr. Technol.
**2010**, 39, 57. [Google Scholar] - Zhang, K.; Li, J. Accident analysis for “08.11.15” foundation pit collapse of Xianghu station of Hangzhou metro. Chin. J. Geotech. Eng.
**2010**, 32, 338–342. [Google Scholar] - Costa, R.; Valdez, J.; Oliveira, S.; da Silva, L.S.; Bayo, E. Experimental behaviour of 3D end-plate beam-to-column bolted steel joints. Eng. Struct.
**2019**, 188, 277–289. [Google Scholar] [CrossRef] - Gil-Martín, L.M.; Hernández-Montes, E.; Shin, M.; Aschheim, M. Developments in excavation bracing systems. Tunn. Undergr. Space Technol.
**2012**, 31, 107–116. [Google Scholar] [CrossRef] - Ataei, A.; Bradford, M.A.; Valipour, H.R.; Liu, X. Experimental study of sustainable high strength steel flush end plate beam-to-column composite joints with deconstructable bolted shear connectors. Eng. Struct.
**2016**, 123, 124–140. [Google Scholar] [CrossRef] - Grimsmo, E.L.; Clausen, A.H.; Langseth, M.; Aalberg, A. An experimental study of static and dynamic behaviour of bolted end-plate joints of steel. Int. J. Impact Eng.
**2015**, 85, 132–145. [Google Scholar] [CrossRef] [Green Version] - Iwicki, P.; Wójcik, M.; Tejchman, J. Failure of cylindrical steel silos composed of corrugated sheets and columns and repair methods using a sensitivity analysis. Eng. Fail. Anal.
**2011**, 18, 2064–2083. [Google Scholar] [CrossRef] - Peng, L.; Guo, X.; Huang, Z.; Xiong, Z.; Yang, S. Experimental studies on behaviour of bolted ball-cylinder joints under axial force. Steel Compos. Struct.
**2016**, 21, 137–156. [Google Scholar] - Guo, X.; Huang, Z.; Xiong, Z.; Yang, S.; Peng, L. Numerical studies on behaviour of bolted ball-cylinder joint under axial force. Steel Compos. Struct.
**2016**, 20, 1323–1343. [Google Scholar] [CrossRef] - Zeng, Q.; Guo, X.; Huang, Z.; Zong, S. Uniaxial compression bearing capacity of bolted ball-cylinder joint. Eng. Struct.
**2019**, 183, 976–986. [Google Scholar] [CrossRef] - Guo, X.; Xiong, Z.; Luo, Y.; Qiu, L.; Liu, J. Experimental investigation on the semi-rigid behaviour of aluminium alloy gusset joints. Thin Walled Struct.
**2015**, 87, 30–40. [Google Scholar] [CrossRef] - Wang, S.; Zhang, Y.; L, J. Field test verification of new flexible head steel support and deep foundation excavation support effect. Constr. Technol.
**2019**, 48, 72–77. [Google Scholar] - Zhang, M.; Xie, Z.; Liu, Y. Mechanical properties and improvement measures of the active node in steel braced foundation pit engineering for subway. J. Beijing Jiaotong Univ.
**2019**, 43, 66–73. [Google Scholar] - Zhang, M.; Yang, M.; Wang, X. Innovative study on active node of steel tube bracing system for braced excavations. Eng. Mech.
**2018**, 35, 88–94. [Google Scholar] - Editorial Group. GB 50017-2017, Code for Design of Steel Structures; Ministry of Housing and Urbanrural Development of the People’s Republic of China: Beijing, China; General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China: Beijing, China, 2017.
- Zhang, M.; Yang, M.; Li, P. Field application and experimental verification of dismountable double-section BFW active nodes for braced excavations. In Proceedings of the 13th Chinese National Conference on Soil Mechanics and Geotechnical Engineering (CNCSMGE), Tianjin, China, 18–21 July 2019; Volume 2, pp. 437–446. [Google Scholar]
- Editorial Group. GB T699-2015, Quality Carbon Structure Steels; General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China: Beijing, China; Standardization Administration of the People’s Republic of China: Beijing, China, 2015.
- Cheng, D. Handbook of Mechanical Design; Chemical Industry Press: Beijing, China, 2016. [Google Scholar]
- Sultan, A.; John, P.; Nikolaos, N. Time-dependent behaviour of cracked, partially bonded reinforced concrete beams under repeated and sustained loads. Eng. Struct.
**2018**, 163, 267–280. [Google Scholar] - Li, P.; Zou, H.; Wang, F.; Xiong, H. An analytical mechanism of limit support pressure on cutting face for deep tunnels in the sand. Comput. Geotech.
**2020**, 119, 103372. [Google Scholar] [CrossRef] - Zhang, M.; Li, S.; Li, P. Numerical analysis of ground displacement and segmental stress and influence of yaw excavation loadings for a curved shield tunnel. Comput. Geotech.
**2020**, 118, 103325. [Google Scholar] [CrossRef]

Specimen | BC_{max} of EP (kN) | Δ_{e} (mm) | BC_{ult} (kN) | Δ_{u} (mm) | YS_{con} (kN) | Stiffness (kN/mm) |
---|---|---|---|---|---|---|

BFW-AJ1 | 2625 | 8.87 | 4021 | 26.76 | 2952 | 295.9 |

BFW-AJ2 | 3065 | 8.67 | 4195 | 17.57 | 3376 | 353.5 |

_{max}of EP is the maximum bearing capacity in the elastic phase, Δ

_{e}is the displacement in the elastic phase, BC

_{ult}is the ultimate bearing capacity, Δ

_{u}is the ultimate displacement, YS

_{con}is the conditional yield strength, and stiffness is the whole specimen’s axial stiffness in the elastic phase.

High-Strength Bolts | Other Components | |
---|---|---|

Young’s modulus E | 2.06 × 10^{5} N/mm^{2} | 2.06 × 10^{5} N/mm^{2} |

Gravimetric density | 7.70 × 10^{−5} N/mm^{3} | 7.70 × 10^{−5} N/mm^{3} |

Poisson ratio ν | 0.3 | 0.3 |

Constitutive model | von Mises | von Mises |

Initial yield stress f_{y} | 355 N/mm^{2} | 900 N/mm^{2} |

Ultimate yield stress f_{u} | 600 N/mm^{2} | 1080 N/mm^{2} |

No. | Master Surface to Slave Surface | Type |
---|---|---|

1 | Wedge seat to splints | Surface-to-surface |

2 | Splints’ heels to base | Surface-to-surface |

3 | Splints to bolts | Surface-to-surface |

4 | Splints to polish round rods | Surface-to-surface |

5 | Base to polish round rods | Surface-to-surface |

6 | Loading plate to end plate | Surface-to-surface |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, M.; Yang, M.; Li, P.; Gao, Y.
Mechanical Behaviors of a Symmetrical Bolt Fasten Wedge Active Joint for Braced Excavations. *Symmetry* **2020**, *12*, 140.
https://doi.org/10.3390/sym12010140

**AMA Style**

Zhang M, Yang M, Li P, Gao Y.
Mechanical Behaviors of a Symmetrical Bolt Fasten Wedge Active Joint for Braced Excavations. *Symmetry*. 2020; 12(1):140.
https://doi.org/10.3390/sym12010140

**Chicago/Turabian Style**

Zhang, Mingju, Meng Yang, Pengfei Li, and Yunhao Gao.
2020. "Mechanical Behaviors of a Symmetrical Bolt Fasten Wedge Active Joint for Braced Excavations" *Symmetry* 12, no. 1: 140.
https://doi.org/10.3390/sym12010140